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ISSN 1088-6850(e) ISSN 0002-9947(p)

Saari's homographic conjecture of the three-body problem

Author(s): Florin Diacu; Toshiaki Fujiwara; Ernesto Pérez-Chavela; Manuele Santoprete
Journal: Trans. Amer. Math. Soc. 360 (2008), 6447-6473.
MSC (2000): Primary 70F10, 70H05
Posted: May 29, 2008
MathSciNet review: 2434294
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Saari's homographic conjecture, which extends a classical statement proposed by Donald Saari in 1970, claims that solutions of the Newtonian -body problem with constant configurational measure are homographic. In other words, if the mutual distances satisfy a certain relationship, the configuration of the particle system may change size and position but not shape. We prove this conjecture for large sets of initial conditions in three-body problems given by homogeneous potentials, including the Newtonian one. Some of our results are true for $n\ge 3$ .

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